The short answer is YES. 

Capital gains are usually considered to be corpus and remain within the trust so, in the case of a simple trust (one that distributes only income, not gains, the trust is responsible for paying tax on those gains along with any recapture (Section 1250 gain).

Thank you.  This would be 1245 property sale of an easement.  Why would a trust ever distribute capital gains (if they could) if it were a simple trust with no income.   If no income there would be no capital gains tax to the trust, correct?  And there would be no reason to even think about an option to distribute them to the beneficiary?

A simple trust does not distribute corpus. If it does, then it's a complex trust and a complex trust may or may not distribute capital gains depending on the trust language and state law.

If the trust has capital gains and does not distribute them, then the trust would be responsible for any tax due on the 1041.

Thank you so much.

What I am asking is that if the trust does not distribute the capital gains and the trust distributed all the income (simple trust) and  has no income kept within the trust it's capital gain rate would be 0% and it would have to pay nothing, because it would be in the 0% tax bracket and below the next tax bracket?

Correct.

Thank you!!